Measurement of $CP$ asymmetries and branching-fraction ratios for $B^{\pm }\to D{K}^{\pm }$ and $D\ddot{I}{€}^{\pm }$ with $D\to K_{\mathrm{S}}^0{K}^{\pm }\ddot{I}{€}^{\mp }$ using Belle and Belle II data

Abstract

We measure $CP$ asymmetries and branching-fraction ratios for $B^{\pm }\to D{K}^{\pm }$ and $D\ddot{I}{€}^{\pm }$ decays with $D\to K_{\mathrm{S}}^0{K}^{\pm }\ddot{I}{€}^{\mp }$, where $D$ is a superposition of $D^0$ and ${\bar{D}}^0$. We use the full data set of the Belle experiment, containing $772\times 10^{6}B\bar{B}$ pairs, and data from the Belle~II experiment, containing $387\times 10^{6}B\bar{B}$ pairs, both collected in electron-positron collisions at the $\hat{I}\yen (4S)$ resonance. Our results provide model-independent information on the unitarity triangle angle $\ddot{I}{•}_3$.

26 pages, 8 figures